ABSTRACT
Let be an n-dimensional linear space over an algebraically closed base field. We provide a general method for classifying, up to equivalence, all bilinear maps such that , in case a classification of bilinear maps when is known. This is equivalent to giving a procedure to classify (up to isomorphism) all n-dimensional algebras with annihilator of dimension n−m from a given classification of m-dimensional algebras. As an example of application, we consider the case in which m = 2.
Acknowledgments
We would like to thank the referee for the detailed reading of this work and for the valuable suggestions to improve the same.
Disclosure statement
No potential conflict of interest was reported by the author(s).